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January 15th, 2013, 07:14 AM   #1
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Lagrange multiplier method

So I solved a problem, but don't really know the purpose...





Could it be that these to points are the maximum points or am I missing something?
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January 15th, 2013, 10:29 AM   #2
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Re: Lagrange multiplier method

We are given the objective function:



subject to the constraint:



The method of Lagrange multipliers then gives us:





Now this implies:







Substituting this into the constraint, we find:







and so:



Although in slightly different form, my result for the critical point agrees with yours. This is the point which maximizes the objective function, or alternately, which minimizes subject to the given constraint.
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